A Wheel of radius 14in. is rotating 0.5 rad/sec. What is the linear speed v, the angular speed in RPM ( rev per min), and the angular speed in deg/sec?
The velocity answer is incorrect. It should be 7in/sec.
v=14in(30rad/1min)=420in/1min(1min/60sec)=420in/60sec=7in/sec
The revolutions per minute and degrees per second are correct. But to further the answer to an approximate degree it would be about 28.648 degrees per second.
Why did the wheel go to therapy? It felt like it had too many "spinning" thoughts!
Now, let's get to your question. To find the linear speed (v) of the wheel, we can use the formula:
v = r * ω
where r represents the radius of the wheel and ω represents the angular speed. In this case, r is 14in and ω is 0.5 rad/sec. Let's compute it:
v = 14in * 0.5 rad/sec = 7in/sec
So, the linear speed of the wheel is 7 inches per second.
To find the angular speed in RPM (rev per min), we can use the formula:
ω (RPM) = ω (rad/sec) * (60 sec/1 min) * (1 rev/2π rad)
ω (RPM) = 0.5 rad/sec * (60 sec/1 min) * (1 rev/2π rad)
ω (RPM) ≈ 4.77 RPM
Therefore, the angular speed of the wheel is approximately 4.77 RPM.
Lastly, to find the angular speed in degrees per second, we can convert ω (rad/sec) to ω (deg/sec). Since there are 360 degrees in a full revolution, we can use the formula:
ω (deg/sec) = ω (rad/sec) * (180 degrees/π rad)
ω (deg/sec) = 0.5 rad/sec * (180 degrees/π rad)
ω (deg/sec) ≈ 28.65 deg/sec
So, the angular speed of the wheel is approximately 28.65 degrees per second.
Hope this answers your question with a twist of humor!
To find the linear speed, angular speed in RPM, and angular speed in deg/sec, we need to use the following formulas:
Linear speed (v) = radius (r) * angular speed (ω)
Angular speed in RPM = angular speed (ω) * (60 / 2π)
Angular speed in deg/sec = angular speed (ω) * (180 / π)
Given:
Radius (r) = 14 inches
Angular speed (ω) = 0.5 rad/sec
Let's calculate each value step by step:
1. Linear speed (v):
Using the formula v = r * ω, substitute the given values:
v = 14 inches * 0.5 rad/sec
v = 7 inches/sec
Therefore, the linear speed is 7 inches/sec.
2. Angular speed in RPM:
Using the formula Angular speed (RPM) = ω * (60 / 2π), substitute the given values:
Angular speed (RPM) = 0.5 rad/sec * (60 / 2π)
Angular speed (RPM) ≈ 4.774 RPM (rounding to three decimal places)
Therefore, the angular speed is approximately 4.774 RPM.
3. Angular speed in deg/sec:
Using the formula Angular speed (deg/sec) = ω * (180 / π), substitute the given values:
Angular speed (deg/sec) = 0.5 rad/sec * (180 / π)
Angular speed (deg/sec) ≈ 28.647 deg/sec (rounding to three decimal places)
Therefore, the angular speed is approximately 28.647 deg/sec.
To summarize:
The linear speed (v) is 7 inches/sec.
The angular speed in RPM is approximately 4.774 RPM.
The angular speed in deg/sec is approximately 28.647 deg/sec.
v = 2π*14in/rev * (.5/2π)rev/s = 28 in/s
.5rad/s * 1rev/2πrad * 60s/min = 4.77 rev/min
.5rad/s * 180°/πrad = 90/π °/s